This invention relates to a means of controlling installations having a dynamic compressor with a turbine driver. The invention relates also to a protective control for a compressor, and more particularly to means for protection from surge and from a dangerously high speed of rotation.
Control systems of dynamic compressors for maintaining a constant discharge pressure have two main functions:
A. Performance control to adjust the speed of rotation of the compressor to the demands of the user's process.
B. Protective control to prevent the installation from dangerous and instable conditions of operation, and thereby to protect both the installation and the process equipment from damage.
With regard to performance control it is noted that all the dynamic compressors have what is commonly called a surge limit or surge line above which the performance of the compressor is instable. Such instability results in pulsations of pressure and flow rate which may cause damage to the compressor.
The surge line is a function of the discharge pressure (P.sub.2) and the flow rate of gas through the compressor (G). The location of the surge line of any given compressor, using the coordinates P.sub.2, G, is also a function of the molecular weight of gas and of the temperature and pressure of gas in the suction.
Assume here and below that the gas entering the compressor has a stable composition. Then the surge limit can be described by the well know equation: EQU H = a (P.sub.2 - P.sub.1), (1)
where:
H = the flow differential in suction; PA1 P.sub.2 = the pressure after the compressor; PA1 P.sub.1 = the pressure before the compressor; PA1 a = constant coefficient. PA1 j = the ordinal number of the component; PA1 i = the number of components; PA1 .tau.j = the time constants, the magnitudes of which differ from the magnitudes T.sub.P on an average by more than on one order of magnitude less.
According to equation (1), in order to protect the compressor from surge it is necessary and sufficient to fulfill the following condition: EQU H .gtoreq. a (P.sub.2 -P.sub.1) (2)
in coordinates P.sub.2, G each point of the surge limit line can be defined also as to the point of intersection of the horizontal line corresponding to some value of P.sub.2, and the curve corresponding to a certain speed of rotation n.
Then the equation of the surge limit will be: EQU n = f (P.sub.2, .gamma.), (3)
where .gamma. is the specific weight of gas in suction.
This method of defining the surge limit can be used in cases when the characteristics of a compressor have slope which is not too small in a zone close to the surge limit. The condition for the safe operation of the compressor in this case can be described by the following relationships: EQU n &gt; f (P.sub.2, .gamma.) (4)
all known antisurge systems protect compressors from surge by letting part of the compressed as into the atmosphere or recirculating it into the suction.
The conditions (2) and (4), however, can be provided, not only by blowing off or recycling part of the gas, but also by appropriately changing the speed of rotation.
Besides surge, there is considerable danger for the compressor and the process using the compressed gas from an increase of the speed of rotation above certain limits.
It is well known that the dynamic parameters of the transient response of the compressor unit depend considerably on the inertia of rotors of both turbine and compressor and on the volume of the delivery network. Therefore, protecting the compressor from dangerous operating conditions should be made with due regard for both these parameters.
All of the above mentioned types of protective controls are generally passive controls until the pre-established limits have been reached.
In addition to the protective controls, a control is also necessary to adapt the compressor speed of rotation to the varying load requirements of the process for which compressor supplies. In order to fulfill this task, the control system of the compressor in the case being described now should maintain the required constant pressure of gas.
Both of the above mentioned functions of the control system of compressors, i.e. limiting its parameters and changing its speed of rotation in accord with the demands of the technological process, can be accomplished by means of two different methods. According to the first and conventional method, the compressor is controlled by several independent sub-systems, each of which is intended to maintain or limit one definite parameter. Each sub-system can include one or several loops connecting successively.
According to this second and improved method of the present invention, a united control system of a compressor includes several control loops connected together by logical elements. This system is built in such a way that, depending on the changing external conditions (for example the demands of the process, the specific weight of gas in suction), the loops will be connected together differently to form the control circuits for controlling corresponding control members.
If, while using the first conventional method of maintaining constant pressure, the resistance of the net of delivery of the compressor changes, then one of the parameters (the speed of rotation, or the output) can reach the permissible limit. At this moment that control loop which maintains the pressure, (and which henceforth will be called "the main control loop") and the control loop which limits one of the above mentioned parameters will begin to operate simultaneously and this continues until the moment when the output signal of the main control loop reaches saturation.
It is evident that during all of these periods of the common operation of these two loops until saturation, the main control loop, while maintaining the main parameter, prevents the other control loop from adequately protecting the compressor from approaching to the danger zone. While it is true that during the period of the common operation of the main control loop and the protective control for speed (usually short term) the steady state position of the operational point on the field of characteristics of compressor changes insignificantly (which is a positive factor); but, in contrast, the transient response of the control system moves the operational point towards or into a dangerous zone of operation.
After saturation or switching of the output signal of the main control loop, the compressor stays only under the protective control for speed, and under further growth of resistance of net delivery, nothing can prevent the compressor from moving towards the surge limit line. Thus, a fast growth of the resistance of the net can lead to dangerous consequences.
The above mentioned disadvantages may be eliminated by using a second and improved method which can be accomplished by means of a cascade control.
The cascade control system is a multi-loop system. Each loop of this system has a separate controller which is adjusted according to the transfer function of the controlled object, an input signal of the object being at the same time the output signal of the above mentioned controller and the output signal of the controlled object being the controlled parameter maintained or limited by this controller.
The number of successively connected loops can change, for example, by means of logical elements, and this number in each particular case depends on the number of the controlled or limited parameters.
According to the principal of cascade control, the loops are connected successively and in such a way that the output signal of the first loop controls some control member and the output signal of each outer loop is at the same time the input signal for the following loop.
The method of cascade control permits limiting separate controlled parameters simply and also compensating for the influence of large time constants. As a result, this makes it possible to protect the compressor unit from dangerous operational conditions with considerably higher reliability.
To illustrate this point examination of the compensation for a large time constant will be made by considering the following simple examples.
1. Assume that the controlled object has only one accumulator of energy, an aperiodical component with the transfer function: ##EQU1##
It is evident that for full compensation of the time constant T.sub.p, the controller connected directly to a controlled object should have the following transfer function of the proportional-plus-derivative component: EQU G.sub.e.sup.P.I.D. (s) = T.sub.p s+1 (6)
Physically this means that for momentary changes in the output signal of the controlled object, it is necessary to feed to its input a signal with an infinitely great amplitude. It follows from the above that full compensation is unrealizable in real systems with limited resources.
It is important to add that the degree of compensation is limited not only by the energy sources, but also by the conditions of the noise stability. This is because a considerable increase in the degree of compensation is usually connected with a corresponding increase in interference sensitivity.
The real and sufficient compensation can be achieved by the well known proportional-plus-reset controller having following transfer function: ##EQU2##
The time constant Te and coefficient k.sub.e should be selected so that: EQU T.sub.e = T.sub.p and k.sub.e = k.sub.p
Then the transfer function of the open and closed control loops may be simply reduced to the following form: ##EQU3##
2. If the controlled object has not one, but two successively connected aperiodic components, the compensation can be achieved by means of well known proportional-plus-integral-plus-derivative controller with following transfer function: ##EQU4##
Real controlled objects in the majority of cases are sets of aperiodic components. Their time constants can differ by several orders of magnitudes. For practical purposes, however, it is usually sufficient to compensate for the influence of only those time constants of the highest order of magnitude. The transfer function of real object can be represented, for example, in the following form: ##EQU5## where: EQU .pi. (.tau.j s + 1) = (.tau..sub.1 s + 1) . (.tau..sub.2 s + 1) . . . (.tau.is + 1);
where:
Then, as mentioned above, it is sufficient to compensate only the time constant T.sub.P.
In this case the transfer function of the closed loop (with the control feedback) can be simply transformed to the following form, ##EQU6##
The magnitude of T.sub.o (Equation 12) is selected according to the conditions of stability: ##EQU7## Without great error we can make the following approximation: ##EQU8## Where: ##EQU9##
Correspondingly, the transfer function of the open and closed control loops will obtain the following form: ##EQU10##
In other words, the compensation in the above examples is accomplished by the replacement of the open loop having a large time constant with a closed loop having a small time constant.
As it follows from the formula (13), the magnitude of the above mentioned time constant is selected with due regard for the sum of the time constants which are not subjected to the compensation.
Therefore, the problems of controlling the dynamic compressor can be solved by means of this invention, which provides for a cascade control of the parameters of the compressor, a limiting of the minimal admissible flow rate through it, and a limiting of the speed of rotation and of the discharge pressure.